Optical Dispersion Compensation in the Electrical Domain in an Optical Communications System

ABSTRACT

A compensation function mitigates a substantial portion of the chromatic dispersion imparted to a communications signal by an optical communications system. A digital input signal is digitally processed using the compensation function to generate a predistorted signal. An amplitude and a phase of an optical signal are modulated using a pair of orthogonal signal components to generate a predistorted optical signal for transmission. In one implementation, the pair of orthogonal signal components are components of the predistorted signal. In another implementation, the predistorted signal is processed using a non-linear compensator to generate a further distorted signal and the pair of orthogonal signal components are components of the further distorted signal. In that implementation, the non-linear compensator is configured to substantially compensate for nonlinearities in one or both of an optical modulator of a transmitter of the system and an optical-to-electrical converter of a receiver of the system.

TECHNICAL FIELD

The present invention relates to optical communications systems, and inparticular to electrical domain compensation of optical dispersion in anoptical communications system.

BACKGROUND

Optical communications systems typically include a pair of network nodesconnected by an optical waveguide (i.e., fiber) link. Within eachnetwork node, communications signals are converted into electricalsignals for signal regeneration and/or routing, and converted intooptical signals for transmission through an optical link to anothernode. The optical link between the network nodes is typically made up ofmultiple concatenated optical components, including one or more (andpossibly 20 or more) optical fiber spans (e.g., of 40-150 km in length)interconnected by optical amplifiers.

The use of concatenated optical components within a link enablesimproved signal reach (that is, the distance that an optical signal canbe conveyed before being reconverted into electrical form forregeneration). Thus, for example, optical signals are progressivelyattenuated as they propagate through a span, and amplified by an opticalamplifier (e.g., an Erbium Doped Fiber Amplifier—IEDFA) prior to beinglaunched into the next span. However, signal degradation due to noiseand dispersion effects increase as the signal propagates through thefiber. Consequently, noise and dispersion degradation become significantlimiting factors of the maximum possible signal reach.

Dispersion, also known as Group Velocity Dispersion or ChromaticDispersion, in single mode fibre at least, occurs as a result of twomechanisms: a) Waveguide dispersion—within a single mode fibre,different wavelengths travel along the fibre at different speeds; and b)Material dispersion—the phase velocity of plane waves in glass varieswith wavelength. For the purposes of the present invention, referencesto “dispersion” shall be understood to mean the sum total of groupvelocity dispersion effects.

Mathematically, first order dispersion is the derivative of the timedelay of the optical path with respect to wavelength. The effect ofdispersion is measured in picoseconds arrival time spread per nanometre‘line width’ per kilometer length (ps nm⁻¹ km⁻¹). The magnitude ofwaveguide and material dispersions both vary with wavelength, and atsome wavelengths the two effects act in opposite senses. The amount ofdispersion present in a link can also vary with the temperature of thecable, and if the route is changed (e.g., using optical switches).Dispersion in optical fibre presents serious problems when using lightsources whose spectrum is non-ideal, for example broad ormultispectral-line, or when high data rates are required, e.g., over 2GB/s.

For the purposes of analyzing the effects of dispersion, it isconvenient to represent an optical communications system using the blockdiagram of FIG. 1. In this case, the transmitter is represented by anelectrical-to-optical converter (E/O) 2 which operates to convert anelectrical input signal x(t) into a corresponding optical signalE_(IN)(ω) for transmission to the receiver. The optical fiber span 4,including all concatenated components, is represented by a transferfunction T(ω), which will normally be complex. The receiver isrepresented by an optical-to-electrical converter (O/E) 6 which detectsthe optical signal E_(OUT)(ω) received through the optical fiber span 4,and generates a corresponding output signal y(t). For a linear opticalchannel, the received optical signal E_(OUT)(ω) will nominally beequivalent to the product of E_(IN)(ω) and T(ω).

In general, the output signal y(t) represents a distorted version of theinput data signal x(t). While it would be highly desirable for T(ω)=≈1,this is rarely the case. Accordingly, it is frequently necessary toutilize at least some form of compensation, so that the original inputdata signal x(t) can be detected within the distorted output signaly(t).

One commonly used method of addressing the problem of dispersion inhigh-bandwidth communications systems is by inserting one or moreoptical dispersion compensators 8, represented in FIG. 1B by thecompensation function C(ω), within the link. Such dispersioncompensators may, for example, take the form of a length of fibre, aMach Zehnder interferometer, an optical resonator, or a Bragg reflector.Some of these compensators can also produce a controllable amount ofcompensation, which enables mitigation of time-variant dispersioneffects. In either case, these compensators are intended to at leastpartially offset the signal distortions introduced by the systemtransfer function T(ω). The compensation function C(ω) is a dispersivefunction that is selected to optimize performance of the link. In afully linear system, the compensation function C(ω) would preferably beequivalent to the complex conjugate T*(ω) of the transfer function T(ω),in which case T(ω)·C(ω)=1, and the combined effect of T(ω) andC(ω)=T*(ω) would be an undistorted received signal EouT(ω) that exactlycorresponds to the original optical signal E_(IN)(ω). However,limitations of optical components, and the time-varying amount ofcompensation required, make this objective very difficult to achieve.Additionally, optical compensators are expensive and introducesignificant optical losses. These losses must be offset by additionaloptical gain which introduces more optical noise. The additional (orhigher-performance) optical amplifiers required to provide thisincreased gain further increases the total cost of the communicationssystem. In addition, the presence of optical dispersion compensators andhigh performance amplifiers distributed along the length of the linkprovides a significant technical barrier to system evolution. Forexample, implementation of optical switching (e.g. at the Tx and/or Rxends of the link, or an intermediate site without electricaltermination) necessarily requires adjustment of optical amplifiers, inorder to accommodate changing energy states within the link.

These problems can be alleviated by moving the compensation function tothe terminal ends (e.g., the transmitter 2 and/or receiver 6) of thelink. This technique typically involves “preprocessing” the input signalx(t) at the transmitter (Tx) end of the link 4 to improve dispersiontolerance, and/or postprocessing the output signal y(t) detected at thereceiver (Rx) end of the link to accurately detect the input signal x(t)within the distorted output signal y(t).

For example, high bandwidth traffic can be distributed over a largernumber of lower-rate channels. The reduced bit-rate of each channelenhances the dispersion tolerance in proportion to the square of thereduction in the bit-rate. However, this approach is expensive,spectrally inefficient, and creates four wave mixing problems.

The publication “Dispersion Compensation by Active Predistorted SignalSynthesis” Koch et al, Journal of Lightwave Tech, Vol. LT-3, No. 4,August 1985, pp. 800-805, describes a technique for synthesizing apredistorted optical signal at the input end of the optical link.According to Koch et al, an (electrical) input signal is used to drive aset of N parallel optical modulators. Each of the parallel opticalsignals is subject to a respective predetermined delay, and the delayedsignals optically combined to produce a predistorted optical signal.Dispersion of the optical link then processes the predistorted opticalsignal to generate a substantially undistorted optical signal at thereceiver end of the link. This approach uses multiple parallel opticalmodulators, optical delays and a signal combiner to produce anapproximation of the desired “ideal” predistorted optical signal. Theaccuracy of this approximation can be increased by increasing the number(N) of modulators. However, this solution dramatically increases thecost of the system. In addition, in order to compensate time-varyingdispersion, it is necessary to individually control each of the opticalmodulators and the respective signal delays. This requirement cansignificantly increase the size and complexity of the control system.

Koch et al speculate (at page 801) that it might be possible tosynthesize a predistorted waveform using “ . . . an algorithm at theinput which involves all the neighboring bits of information over a timespan on the order of that to which dispersion broadens the sharpestfeatures in the absence of any compensation.” However, Koch et al do notprovide any teaching regarding how this might be accomplished, and infact conclude that this solution would be “ . . . difficult to realize,and in general also requires modulation bandwidths fully capable oftransporting the undistorted signal.” Accordingly, Koch et al rejectthis approach in favor of their technique of combining multiple delayedoptical signals.

Dispersion tolerance can be increased by narrowing the spectrum of thetransmitted optical signal. Various known techniques may be used forthis purpose, such as multilevel coding. However, this requiresexpensive electronics and significantly reduces the noise tolerance ofthe communications system.

Subcarrier multiplexing, which involves transmitting a plurality oflower bit-rate signals over one optical carrier, is another known methodof increasing dispersion tolerance. In this case, the dispersiontolerance obtained is equivalent to that of the lower bit-ratesubcarrier, However this approach is not cost effective and does nothave a good noise tolerance.

The optical spectrum occupied by a signal can be reduced by use ofmodulators with reduced chirp, such as a Mach-Zehnder modulator. Theamount of chirp can even be tailored to optimize transmission over aparticular moderate amount of dispersion. One variation of thistechnique is referred to as dispersion supported transmission, anexample of which is discussed in EP-A-0643 497. In this case, dispersionproduces an FM to AM conversion effect, which can facilitate bitdetection and thereby extend transmission distance without controllingor compensating dispersion. The dispersion causes shifting of adjacentsignal components of different wavelengths, resulting in either energyvoids or energy overlaps at the bit transitions. Constructiveinterference in an overlap causes a positive peak in the optical signal,while a void produces a negative peak. In principle, these positive andnegative peaks represent an AM signal which may be detected to reproducethe original bit stream, This has proved difficult to implement over areasonable range of practical link dispersions.

Many transmission formats are known that enable somewhat increaseddispersion tolerance, for example, as described in U.S. Pat. No.5,892,858. However none of these formats provide sufficient dispersiontolerance to allow a wide bandwidth signal to be accurately detected inthe presence of large amounts of dispersion.

It is known that the use of a coherent receiver enables the signaldegradation due to dispersion to be removed via linear electricalfiltering. However, because of their high cost, very few coherentoptical receivers have been installed, and the cost of replacinginstalled receivers with the high-performance coherent receivers isprohibitive.

The majority of receivers installed in modern optical communicationsnetworks are of the direct detection type. Due to the well knownsquaring effect in these receivers, electrical processing of the outputsignal y(t) is capable of compensating only a very limited amount ofdispersion. See, for example, “Performance of Smart Lightwave Receiverswith Linear Equalization” Cartledge et al, J Lightwave Tech, Vol. 10,No. 8, August 1992, pp. 1105-1109; and “Electrical Signal ProcessingTechniques in Long-Haul Fiber-Optic Systems” Winters et al, IEEE Trans.Comms, Vol. 38, No. 9, September 1990, pp. 1439-1453.

In addition to the squaring effect in conventional receivers, opticalmodulators also frequently display a non-linear performancecharacteristic. Nonlinearity compensation of modulators can beimplemented in the electrical domain (see, for example “Reduction ofDispersion-Induced Distortion in SCM Transmission Systems by usingPredistortion-Linearized MOW-EA Modulators”, Iwai et al, Journal ofLightwave Tech., Vol. 15, No. 2, February 1997, pp. 169-177). It is alsopossible to provide the nonlinear compensation in the optical domain(see “Mitigation of Dispersion-Induced Effects using SOA in AnalogOptical Transmission”, Jeon et al, IEEE Photonics Technology Letters,Vol. 14, No 8, August 2002, pp. 1166-1168 and “Predistortion Techniquesfor Linearization of External Modulators”, Wilson, 1999 Digest of theLEOS Summer Topical Meetings, 1999, pp. IV39-IV40), or via hybridoptical/electrical domains (see, for example “Signal Distortion andNoise in AM-SCM Transmission Systems employing the FeedforwardLinearized MQW-EA External Modulator”, Iwai et al, Journal of LightwaveTech., Vol. 13, No. 8, August 1995, pp. 1606-1612 and U.S. Pat. No.5,148,503).

While modulator non-linearity can be compensated, the output signal y(t)detected at the Rx end of the communications system contains distortioncomponents due to non-linearities in both the modulator (transmitter) 2and the receiver 6, as well due to optical dispersion within the link 4.These distortions are compounded, one upon the other, and it isdifficult to distinguish distortions of the output signal y(t) due tonon-linearity of the modulator 2 from those resulting from non-linearityof the receiver 6. It is also difficult to distinguish these effectsfrom dispersion.

Accordingly, a cost-effective technique for mitigating the effects ofdispersion on high bandwidth optical signals remains highly desirable.

SUMMARY OF THE INVENTION

Accordingly, an object of the present invention is to provide atechnique for mitigating effects of dispersion on high bandwidth opticalsignals in an optical communications system.

This object is met by the combination of elements defined in theappended independent claims. Option elements of the invention aredefined in the dependent claims.

Thus an aspect of the present invention provides a method ofcompensating optical dispersion of a communications signal conveyedthrough an optical communications system. A compensation function isdetermined that substantially mitigates the chromatic dispersionimparted to the communications signal by the optical communicationssystem. The communications signal is then modulated in the electricaldomain using the compensation function.

The method of the invention can be implemented at either the Tx or Rxends of the communications system, or may be divided between both ends,as desired. In cases where the method of the invention is implemented inthe transmitter, the communication signal in the form of an inputelectrical signal (e.g. a substantially undistorted binary signal) isdigitally filtered using the compensation function to generate apredistorted signal. The predistorted signal is then used to modulate anoptical source to generate a corresponding predistorted optical signalfor transmission through the optical communications system. Thisarrangement is particularly advantageous, because the predistortedsignal can incorporate compensation for dispersion and component non-lineariti es throughout the system. Consequently, dispersion compensationcan be effectively implemented independently of the type of detection .. direct or coherent) used in the receiver.

In cases where the method of the invention is implemented in thereceiver, the received optical signal is converted into a correspondingreceived electrical signal, which includes distortions due to dispersionimparted on the optical signal by the optical communications system. Thereceived electrical signal is then sampled (e.g. using ananalog-to-digital converter) and digitally filtered using thecompensation function to generate an output electrical signal which is asubstantially undistorted version of the original communications signal.

Thus the present invention compensates optical dispersion by digitallyfiltering a communications signal in the electrical domain. Thisfiltering of the communications signal is governed in accordance withthe required compensation function of the communications system transferfunction and the non-linearity compensation required. With thisarrangement, arbitrary optical dispersion imparted by the communicationssystem can be compensated in such a manner that a comparativelyundistorted output signal is generated at the receiving end of thecommunications system.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIGS. 1A and 1B are block diagrams schematically illustratingtransmission of an input data signal through a conventional opticalcommunications system;

FIG. 2 is a block diagram schematically illustrating transmission of aninput signal through an optical communications system in accordance withan embodiment of the present invention;

FIG. 3 is a block diagram schematically illustrating principalcomponents and operations of a compensation processor in accordance witha first embodiment of the present invention.

FIG. 4 is a block diagram schematically illustrating principalcomponents and operations of a compensation processor in accordance witha second embodiment of the present invention;

FIG. 5 is a block diagram schematically illustrating principalcomponents and operations of a compensation processor in accordance witha third embodiment of the present invention;

FIGS. 6A and 6B are block diagrams schematically illustrating principalcomponents and operations of a compensation processor in accordance witha fourth embodiment of the present invention; and

FIGS. 7A and 7B are block diagrams schematically illustrating principalcomponents and operations of a compensation processor in accordance witha fifth embodiment of the present invention.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention provides a method and system for compensation ofchromatic dispersion in an optical communications system. FIG. 2 is ablock diagram schematically illustrating principal operations inaccordance with the method of the present invention.

As shown in FIG. 2, the optical communications system is represented byelectrical-to-optical (E/O) and optical-to-electrical (O/E) converters 2and 6 separated by an optical link 4 represented by a system transferfunction T(ω). In accordance with the present invention, signaldistortions introduced by the system transfer function T (ω) arecompensated by deriving a compensation function C(ω) that optimizessystem performance. A compensation processor 10 uses the compensationfunction C(ω) to filter the input signal x(t) in the electrical domain,thereby producing a predistorted input signal x¹(t) 12 given byx¹(t)=x(t) conv C(ω) where “conv” is the convolution function,

The predistorted input signal x¹(t) 12 is then converted to acorresponding predistorted optical signal E¹ _(IN)(ω) by the E/Oconverter 2 and transmitted through the optical link 4 to the receiver.Within the receiver, the incoming optical signal E¹ _(OUT)(ω) isconverted by the O/E converter 6 into a corresponding output signaly¹(t). As may be seen in FIG. 2, the received. optical signal E¹_(OUT)(ω) is the predistorted optical signal E′_(IN)(ω) multiplied bythe transfer function T(ω) of the optical communications system. Whenthe distortions introduced by the compensation function C(ω) exactlycounterbalance those introduced by the system transfer function T(ω),the output signal y¹(t) generated by the O/E converter 6 will be asubstantially undistorted version of the original input data signalx(t). Thus the present invention provides a technique of compensatingoptical distortions impressed upon optical signals traversing theoptical link 4, by predistorting the input data signal x(t) in theelectrical domain at the transmitting end of the optical link 4. Becausedispersion compensation is accomplished in the electrical domain, asubstantially arbitrary compensation function C(ω) can be implemented,thereby facilitating effective compensation of even severe opticaldispersion.

Various methods may be used to derive the compensation function C(ω). Inthe example of FIG. 2, the optical signal E¹ _(OUT)(ω) at or near theO/E converter 6 is monitored (at 14), in order to detect signal qualityparameters indicative of dispersion in the optical communicationssystem. in preferred embodiments, the signal quality parameters comprisea direct measurement of dispersion as a function of wavelength acrossthe wavelength band of interest. However, other signal qualityparameters such as, for example, the bit error rate or eye closure maybe used as proxies for the dispersion. Any of the signal qualityparameters may be detected based on an optical signal obtained bytapping the optical link 4 (as shown by solid lines in FIG. 2), oralternatively by analysis of the output signal y(t) generated by the E/Oconverter 6 (as shown by the dashed line in FIG. 2), In either case, acompensation function C(ω) which optimizes the detected parameters canthen be derived (at 16) deterministically and/or adaptively, using knowntechniques.

It should be noted that the functional step of deriving the compensationfunction C(ω) can be implemented by any suitable combination of hardwareand software, which may be co-located with the receiver, thetransmitter, or any other location. In embodiments in which the detectedparameters comprise direct measurement of dispersion, the compensationfunction C(ω) can be derived to minimize (and preferably eliminate) thetotal dispersion. Where bit error rate and/or eye closure are used asproxies, then the compensation function C(ω) would be derived tooptimize these values.

FIG. 3 is a block diagram schematically illustrating principal elementsand operations of the compensation processor 10, in accordance with afirst embodiment of the present invention. As shown in FIG. 3, the inputsignal x(t) is filtered by a digital filter 18 which accepts thecompensation function C(ω) as an input. Various known digital filtertypes may be used to implement the digital filter 18, such as, forexample, Finite Impulse Response (FIR) filters, Infinite ImpulseResponse (DR) filters, and Fast Fourier Transform (FFT filters).Alternatively, the digital filter 18 may be implemented using a RandomAccess Memory Look-up Table (RAM LUT), as will be described in greaterdetail below with reference to FIGS. 4-7. In either case, the digitalfilter 18 generates successive sample values 20 of the predistortedsignal x¹(t) 12, at a sample rate which is about double the bit-rate ofthe input signal. A high-speed digital to analog converter (DAC) 22 canthen be used to convert these sample values 20 into an analogpredistorted signal x¹(t) 12. If desired, the analog predistorted signalx¹(t) 12 can be conditioned, for example by means of a filter 24 and alow noise amplifier (LNA) 26, in a conventional manner, to removeout-of-band noise and to scale the amplitude of the analog signal to thedynamic range of the E/O converter 2. In the illustrated embodiment, theE/O converter 2 comprises a tuned optical source 28 such as a narrowband laser coupled to a conventional optical modulator 30. In this case,the analog predistorted signal x¹(t) 12 can be used as an input tocontrol the optical modulator 30 in a manner known in the art.

As mentioned above, the digital filter 18 may be implemented in avariety of ways. FIG. 4 schematically illustrates an embodiment in whichthe digital filter 18 is implemented using a RAM LUT 32. This techniqueexploits the fact that the input signal x(t) is a substantiallyundistorted binary signal, in which successive bits can be unambiguouslydiscriminated. This greatly simplifies the problem of digitallyfiltering the input signal x(t), because a direct relationship can bedefined between the input signal x(t) and each sample value 20 of thepredistorted signal x¹(t) 12.

As shown in FIG. 4, successive bits of the input signal x(t) are latchedthrough a serial-to-parallel converter (SPC) 34 (e.g., a shift register)which converts the serial bit stream into a parallel bit stream 36having a width of N bits. In the illustrated embodiment N=8, it beingunderstood that other values of N may be used as desired. Each N-bitword of the parallel data stream 36 is then used as an index value toaccess a random access memory (RAM) look-up table 32 having 2^(N)registers (not shown). With this arrangement, one or more M-bit (where Mwill generally be at least four) sample values 20 of the predistortedsignal x¹(t) 12 corresponding to each N-bit word can be calculated andstored in each register of the RAM LUT. As each N-bit word of theparallel data stream is latched into the RAM LUT, the correspondingM-bit sample value(s) of the predistorted signal x¹(t) 12 is (are)latched out of the RAM LUT 32. It should be noted that, in order tofacilitate accurate synthesis of the predistorted signal x¹(t) 12 at theoutput of the DAC 22, the Nyquist sampling theorem must be respected. Inthis case, each register of the RAM LUT 32 will store at least twosuccessive sample values 20 for each N-bit word of the parallel datastream. Because the RAM LUT 32 performs a substantially linear filteringfunction, it is possible to construct the LUT 32 as a set of two or moreRandom Access Memory blocks (not shown), if desired. In this case, eachRAM block stores a respective portion of the desired numerical value 20of the predistorted signal component. Thus the outputs generated fromeach RAM block can be digitally summed, in a conventional manner, toproduce the desired numerical value 20. This arrangement allows the LUT32 to be larger than can conveniently be accommodated within a singleRAM block.

Various methods may be used to calculate each of the digital values 20stored in the look-up table 32. In the example of FIG. 4, thecompensation function C(ω) (derived at 16) is used to calculate (at 38)respective M-bit sample values for each of the 2^(N) possible N-bitwords. Each M-bit sample value can then be stored in the appropriate RAMLUT register indexed by its respective N-bit word.

Because chromatic dispersion causes a time domain distortion of an inputsignal, the sample value of the predistorted input signal 12 at aparticular instant (t) will necessarily be a function of the analogwaveform of the input signal x(t) within a time window that brackets theinstant in question. The width of the time window, measured in symbols,will generally be a function of the maximum dispersion (D) for whichcompensation is to be provided; the bandwidth (B) of the optical signal;and the symbol interval (S) of the optical signal. For example, consideran optical communications system in which the transmitter generates anoptical signal having a bandwidth of B nanometers and a symbol intervalof S picoseconds/symbol. In this case, the maximum dispersion (D) thatcan be compensated is given by the equation D=N·(S/B), where N is thewidth of the time window, measured in symbols. It will be appreciatedthat the selected value of N will limit the maximum dispersion (D) thatcan be effectively compensated. In general, the value of N will beselected based on the expected maximum dispersion of the opticalcommunications system.

In the example of FIGS. 3 and 4, the look-up table 32 uses N=8successive bits of the input signal x(t) to reference successive samplevalues 20 of the predistorted signal 12. In this case, the time windowused for calculating each sample value of the predistorted signal spansa total of N=8 symbols.

Following the discussion above, it will be seen that each sample value20 stored in the look-up table 32 can readily be calculated (at 38) byapplying the derived compensation function C(ω) to each one of the 2.possible N-hit words. For each N-bit word, the calculated sample valuecan then be stored in the lookup table register that is indexed by theN-bit word in question. This process will result in the look-up table 32being loaded with pre-calculated sample values 20 of the predistortedsignal 12 which will be accessed, in sequence, as successive bits of theinput signal x(t) are latched through the serial-to-parallel converter34.

It will generally be advantageous to arrange the RAM LUT 32 to outputmore than one numerical value 20 of the predistorted signal 12 for eachbit of the input signal x(t). This can readily be accomplished bycalculating the required numerical values 20 for each N-bit word, andstoring the resulting set of numerical values 20 in the appropriateregister. As each bit of the input signal x(t) is latched through theserial-to-parallel converter 34, all of the numerical values calculatedfor each unique N-bit word will be output, in an appropriate sequence,from the RAM LUT 32.

In the foregoing discussion, it was assumed that both the DAC 22 and theoptical modulator 30 are fully linear, so that these components do notintroduce any distortions beyond those accounted for by the systemtransfer function T(ω). Depending on how the system transfer functionT(ω) is defined, this approach may yield satisfactory results. However,it may be desirable to treat the transfer function T(ω) of the opticalfiber span 4 separately from those of the DAC 22 and modulator 30, inwhich case the compensation function C(ω) will not account fordistortions introduced by these elements.

In many cases, the performance of the various devices forming the signalpath between the DAC 22 and modulator 30, (i.e. the DAC 22, filter 24,LNA 26 and modulator 30) are well characterized, and this knowledge canbe used to calculate a mapping which adjusts the sample values 20generated by the RAM LUT 32 to compensate for any non-ideal response ofthese devices. However, improved performance can be obtained by samplingthe optical waveform output from the E/O converter 2, and comparing theinstantaneous amplitude of the optical waveform with the correspondingsample value output by the RAM LUT. Thus, as shown in FIG. 4, theoptical waveform output from the E/O converter 2 is tapped (at 40),converted into a corresponding electrical signal (at 42), and sampled byan analog-to-digital (A/D) converter 44. The digital sample 46 generatedby the A/D converter 44 is then supplied to a non-linear processor 48,which also receives sample values 20 of the predistorted signal 12 fromthe RAM LUT 32. By properly accounting for propagation delays, it isreadily possible to match each sample value 20 with its correspondingdigital sample 46 from the AID converter 44. Comparison between thesetwo values (20 and 46) facilitates calculation of a mapping which can beapplied to the sample values 20 to compensate any non-ideal response ofthe entire signal path between (and including) the DAC 22 and the E/Oconverter 2, and thereby yield a desired waveform of the predistortedoptical signal E¹ _(IN)(ω) at the output of the E/O converter 2.

As may be seen in FIG. 4, the mapping calculated by the non-linearprocessor 48 can be used to drive a non-linear compensator 50implemented as a second RAM look-up table positioned between the digitalfilter 18 and the DAC 22. Alternatively, the mapping can be used toadjust (at 52) the M-bit sample values 20 calculated (at 38) using thecompensation function C(ω). In the latter case, sample values 20 outputfrom the digital filter 18 will combine compensation for both dispersionof the link 4 and nonlinearities of the DAC 22 and E/O converter 2.

In the embodiments of FIGS. 3 and 4, a single compensation path isprovided for generating the predistorted signal x¹(t) 12 based on theinput signal x(t). As will be appreciated, such an arrangement issuitable for modulating a single dimension (e.g., either amplitude orphase) of the input signal x(t). Accordingly, the predistorted signalx¹(t) 12 of the embodiments of FIGS. 3 and 4 will comprise an amplitudeor phase modulated version of the original input signal x(t). However,the system transfer function T (ω) of the optical communications systemwill normally be complex, so that an optical signal traversing thecommunications system will suffer distortions in both phase andamplitude. This issue is addressed by the embodiments of FIGS. 5-7.

FIG. 5 is a block diagram schematically illustrating an embodiment ofthe present invention in which a 2-dimensional compensation processor 10is used to compensate effects of a complex system transfer functionT(ω). In general, the 2-dimensional compensation processor 10 providesan independent compensation path for each dimension of thecommunications system for which compensation is to be provided. In theembodiment of FIG. 5, it is desired to provide compensation for bothamplitude and phase distortions. In this case, a pair of compensationpaths generate respective output signals I and Q (at 56 and 58) thatrepresent respective orthogonal (In-phase and Quadrature) components ofthe predistorted signal 12.

The two output signals I and Q are then supplied to a suitable2-dimensional optical modulator 30 capable of modulating the amplitudeand phase of light generated by the optical source 28. Various opticalmodulators capable of providing this functionality are known in the art,such as, for example, Mach Zehnder modulators.

As will be appreciated, the 2-dimensional compensation processor 10 canbe implemented using multiple compensation paths to generate thepredistorted signal x¹(t) 12 in any desired format, such as, forexample, polar coordinates. The only limitation here is that a suitableoptical modulator 30 must be provided for modulating the appropriateoptical components in response to the signal components generated by the2-dimensional compensation processor 10.

FIG. 6A is a block diagram illustrating an alternative embodiment of the2-dimensional compensation processor 10 of FIG. 5. In this case, thepair of parallel N×M RAM LUTs 32 of the digital filter 18 are replacedby a single N×2M look-up table, which outputs parallel M-bit samplevalues 20 for each N-bit sequence of the input data x(t). As in theembodiment of FIG. 5, these M-bit sample values 20 represent respectiveorthogonal (e.g. In-phase and Quadrature) components of the predistortedsignal x¹(t) 12. Similarly, other signal formats, such as polarcoordinates, may equally be used, provided only that the opticalmodulator 30 is capable of modulating the appropriate optical componentsin response to the signals generated by the multi-dimensionalcompensation processor 10.

In the embodiment of FIGS. 4-6, the input signal x(t) is supplieddirectly to the SPC 34, which converts the serial bit stream x(t) intosuccessive N-bit words of the parallel data stream 36. In some cases,however, it may be desirable to provide a converter 64 to map the serialbit stream x(t) into n-bit symbols 66 upstream of the SPC 34, as shownin FIG. 6B. This arrangement would be particularly suitable forQuadrature Phase Shift Keying (QPSK) encoded traffic, for example. insuch cases, the SPC 34 will operate to convert each bit of the n-bitsymbol stream 66 into successive N-bit words of a corresponding paralleldata stream 36. The values stored in each register of the RAM LUT arecalculated to implement a complex filtering operation to outputappropriate parallel M-bit sample values 20 of the predistorted signal12.

Due to various factors (such as, for example imperfections, orelectrical cross-talk) the orthogonal (i.e. In-phase and Quadrature)control signals 56, 58 may in fact produce a non-orthogonal response inthe ED converter 2. Accordingly, in the embodiment of FIG. 6A thenon-linear compensator 50 is provided as a single 2M×2M RAM LUT, insteadof separate devices for each compensation path. Each of the 2^(2M)registers of the non-linear compensator 50 stores previously calculatedoutput numerical values for both control signals 56, 58.

These output numerical values may be calculated in accordance with amapping function derived from the combined lightwave emerging from theE/O converter 2, as described above with reference to FIG. 4, With thisarrangement, the non-linear compensator 50 can readily implement a 2-Dmapping which adjusts both components of the predistorted signal 12 in acomplementary manner, to thereby compensate for any non-orthogonalresponse of the E/O converter 2. As mentioned above, the non-linearcompensator 50 may be implemented as a separate device (from the RAM LUT32), or may be “embedded within the RAM LUT 32” by applying the mappingfunction to adjust the sample values stored in the RAM LUT 32.

As may be appreciated, in order to successfully compensate dispersion ofthe link 4, it is important to maintain precise alignment between eachof the signal components 56, 58 of the predistorted signal x¹(t) 12supplied to the optical modulator 30. However, the effects ofindependent DACs 22, filters 24 and LNAs 26 for each signal componentmay cause differential propagation delays between the non-linearcompensator 50 and the optical modulator 30. Such differential delay canbe compensated by means of a digital filter 60 located in at least oneof the signal paths. In general, for an n-dimensional compensationprocessor 10 (i.e. generating n signal components of the predistortedsignal 12) differential propagation delays can be compensated byproviding a respective digital filter 60 in at least (n−1) compensationpaths. For convenience, it may be desirable to provide a digital filter60 in all of the signal paths, as illustrated in FIG. 6A. In any event,each digital filter 60 can be controlled in a known manner to impose anselected delay, which is calculated to compensate for the differentialpropagation delays experienced by each of the signal components.

If desired, the non-linear compensator 50 can also be used to implementa mapping between different signal formats. For example, in theembodiments of FIGS. 7A and 7B, the digital filter 18 is designed togenerate the predistorted signal x¹(t) 12 in the form of In-phase andQuadrature components. In addition to compensating non-ideal response ofthe signal paths between the DACs 22 and the E/O converter 2, the 2M×2Mmapping implemented in the non-linear compensator 50 may also be used toconvert these I and Q signal components into a corresponding pair ofAmplitude A and Phase φ component samples (i.e. following a polarcoordinate system), as shown in FIG. 7A. Subsequent digital-to-analogconversion of the phase sample by the DAC 22 a yields a phase controlsignal 56 which can be used to drive a conventional phase shifter 62 tomodulate the phase of the optical signal. The amplitude of the opticalsignal can then be controlled using a conventional optical modulator(such as an electroabsorptive modulator (EAM) or a variable opticalattenuator) in accordance with the amplitude control signal component58.

As shown in FIG. 7B, the digital filter 60 a can be controlled tocalculate the time derivative of the phase component, to yield afrequency sample f(n). In embodiments in which the non-linearcompensator 50 is incorporated into the RAM LUT 32, the digital filter18 can generate the predistorted signal x¹(t) 12 in the form ofAmplitude and frequency components directly. In either case, subsequentdigital-to-analog conversion of the frequency sample f(n) by the DAC 22a yields a frequency control signal f(t) 56 which can be used to drivethe optical source 28 directly. This operation exploits the knowncharacteristic of many narrow-band lasers, which exhibit a frequencydependence on the input current. Accordingly, within a certain range,the frequency of the optical signal emitted by the optical source 28 canbe controlled by varying the input current. Here again, the amplitude ofthe optical signal can be controlled using a conventional opticalmodulator (such as an electroabsorptive modulator (EAM) or a variableoptical attenuator) in accordance with the amplitude control signalcomponent 58.

The embodiment(s) of the invention described above is (are) intended tobe exemplary only. The scope of the invention is therefore intended tobe limited solely by the scope of the appended claims.

What is claimed is:
 1. A method of compensating chromatic dispersion ofa communications signal conveyed through an optical communicationssystem, the method comprising: deriving a compensation function thatmitigates a substantial portion of the chromatic dispersion imparted tothe communications signal by the optical communications system;digitally processing a digital input signal using the compensationfunction to generate a. predistorted signal comprising a pair oforthogonal signal components; and modulating an amplitude and a phase ofan optical signal using the pair of orthogonal signal components of thepredistorted signal to generate a corresponding predistorted opticalsignal for transmission through the optical communications system. 2.The method as recited in claim 1, wherein deriving the compensationfunction comprises: detecting one or more performance parametersindicative of the chromatic dispersion; and deriving the compensationfunction which optimizes the detected one or more performanceparameters.
 3. The method as recited in claim 2, wherein the performanceparameters include one or more of: a direct measurement of the chromaticdispersion; a bit error rate; a signal-to-noise ratio; an eye closureratio; a stimulus response; and a probability distribution.
 4. Themethod as recited in claim 2, wherein detecting the performanceparameters indicative of the chromatic dispersion comprises tapping anoptical link of the optical communications system.
 5. The method asrecited in claim 2, wherein detecting the performance parametersindicative of the chromatic dispersion comprises analyzing an outputsignal generated by an optical-to-electric converter in a receiver ofthe optical communications system.
 6. The method as recited in claim 1,further comprising: removing part of the chromatic dispersion via linearelectrical filtering at a coherent receiver of the opticalcommunications system.
 7. A method of compensating chromatic dispersionof a communications signal conveyed through an optical communicationssystem, the method comprising: deriving a compensation function thatmitigates a substantial portion of the chromatic dispersion imparted tothe communications signal by the optical communications system;digitally processing a digital input signal using the compensationfunction to generate a predistorted signal; processing the predistortedsignal using a non-linear compensator to generate a further distortedsignal comprising a pair of orthogonal signal components; and modulatingan amplitude and a phase of an optical signal using the pair oforthogonal signal components of the further distorted signal to generatea corresponding predistorted optical signal for transmission through theoptical communications system, wherein the non-linear compensator isconfigured to substantially compensate for nonlinearities in one or bothof an optical modulator of a transmitter of the optical communicationssystem and an optical-to-electrical converter of a receiver of theoptical communications system.
 8. The method as recited in claim 7,further comprising: removing part of the chromatic dispersion via linearelectrical filtering at a coherent receiver of the opticalcommunications system.
 9. A dispersion compensation system forcompensating chromatic dispersion of a communications signal conveyedthrough an optical communications system, the dispersion compensationsystem comprising: a processor configured to derive a compensationfunction that mitigates a substantial portion of the chromaticdispersion imparted to the communications signal by the opticalcommunications system; a compensation processor configured to digitallyprocess a digital input signal using the compensation function togenerate a predistorted signal comprising a pair of orthogonal signalcomponents; and a multi-dimensional optical modulator configured tomodulate an amplitude and a phase of an optical signal using the pair oforthogonal signal components of the predistorted signal to generate acorresponding predistorted optical signal for transmission through theoptical communications system.
 10. The dispersion compensation system asrecited in claim 9, wherein the compensation processor comprises: a pairof serial-to-parallel converters configured to convert successive bitsof the digital input signal into two parallel bit streams each having awidth of N bits; a pair of random access memory look up tablesconfigured to be accessed by a respective one of the parallel bitstreams and configured to store numerical values of a respective one ofthe pair of orthogonal signal components; and a pair ofdigital-to-analog converters configured to convert streams of successivenumerical values to respective ones of the pair of orthogonal signalcomponents.
 11. The dispersion compensation system as recited in claim9, wherein the processor configured to derive the compensation functioncomprises: a detector configured to tap an optical link of the opticalcommunications system to measure one or more performance parametersindicative of the chromatic dispersion; and a processor configured toderive the compensation function which optimizes the detected one ormore performance parameters.
 12. The dispersion compensation system asrecited in claim 9, wherein the processor configured to derive thecompensation function is configured: to analyze an output signalgenerated by an optical-to-electric converter in a receiver of theoptical communications system to determine one or more performanceparameters indicative of the chromatic dispersion; and to derive thecompensation function which optimizes the one or more performanceparameters.
 13. The dispersion compensation system as recited in claim12, wherein the performance parameters include one or more of: obiterror rate; a signal-to-noise ratio; an eye closure ratio; a stimulusresponse; and a probability distribution.
 14. The dispersioncompensation system as recited in claim 9, further comprising a coherentreceiver configured to remove part of the chromatic dispersion vialinear electrical filtering.
 15. A dispersion compensation system forcompensating chromatic dispersion of a communications signal conveyedthrough an optical communications system, the method comprising: aprocessor configured to derive a compensation function that mitigates asubstantial portion of the chromatic dispersion imparted to thecommunications signal by the optical communications system; acompensation processor configured to digitally process a digital inputsignal using the compensation function to generate a predistortedsignal; a non-linear compensator configured to process the predistortedsignal to generate a further distorted signal comprising a pair oforthogonal signal components; and a multi-dimensional optical modulatorconfigured to modulate an amplitude and a phase of an optical signalusing the pair of orthogonal signal components of the further distortedsignal to generate a corresponding predistorted optical signal fortransmission through the optical communications system, wherein thenon-linear compensator is configured to substantially compensate fornonlinearities in one or both of an optical modulator of a transmitterof the optical communications system and an optical-to-electricalconverter of a receiver of the optical communications system.
 16. Thedispersion compensation system as recited in claim 15, wherein thecompensation processor comprises: a pair of serial-to-parallelconverters configured to convert successive bits of the digital inputsignal into two parallel bit streams each having a width of N bits; apair of random access memory look up tables configured to be accessed bya respective one of the parallel bit streams and configured to storenumerical values of a respective one of the pair of orthogonal signalcomponents; and a pair of digital-to-analog converters configured toconvert streams of successive numerical values to respective ones of thepair of orthogonal signal components.
 17. The dispersion compensationsystem as recited in claim 15, wherein the non-linear compensatorcomprises a nonlinear digital filter.
 18. The dispersion compensationsystem as recited in claim 15, wherein the non-linear compensatorcomprises a nonlinear multiplier.
 19. The dispersion compensation systemas recited in claim 15, wherein the non-linear compensator comprises alook up table.
 20. The dispersion compensation system as recited inclaim 15, further comprising a coherent receiver configured to removepart of the chromatic dispersion via linear electrical filtering.